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3. Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (see A loaded cement mixer drives onto an old figure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an angle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge. T 70° k10.0 m 40.0 m 30 (i) Sketch the free-body diagram (FBD) of the drawbridge with complete force labels. (ii) (iii) Determine the moment arm () of each force. Show complete solution. Put the results in a table. Determine the sign of the torque, based on the direction of rotation of the beam that is caused by each torque. Indicate these on your FBD. Indicate the signs of the torques in the table of results. What is the tension (T) in the cable when the drawbridge is held in this position? What are the horizontal and vertical components of the force the hinge (Fpx and Fpy) exerts on the drawbridge? (iv) (v)

3. Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (see A loaded cement mixer drives onto an old figure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an angle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge. T 70° k10.0 m 40.0 m 30 (i) Sketch the free-body diagram (FBD) of the drawbridge with complete force labels. (ii) (iii) Determine the moment arm () of each force. Show complete solution. Put the results in a table. Determine the sign of the torque, based on the direction of rotation of the beam that is caused by each torque. Indicate these on your FBD. Indicate the signs of the torques in the table of results. What is the tension (T) in the cable when the drawbridge is held in this position? What are the horizontal and vertical components of the force the hinge (Fpx and Fpy) exerts on the drawbridge? (iv) (v)

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3. Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (see A loaded cement mixer drives onto an old figure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an angle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge. T 70° k10.0m 40.0 m 30 (i) Sketch the free-body diagram (FBD) of the drawbridge with complete force labels. (ii) (ii) Determine the moment arm () of each force. Show complete solution. Put the results in a table. Determine the sign of the torque, based on the direction of rotation of the beam that is caused by each torque. Indicate these on your FBD. Indicate the signs of the torques in the table of results. What is the tension (T) in the cable when the drawbridge is held in this position? What are the horizontal and vertical components of the force the hinge (Fpx and Fpy) exerts on the drawbridge? (iv) (v)
Transcribed Image Text:3. Rigid-Body in Equilibrium: A Truck on a Drawbridge. drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help, sets the handbrake, and waits. Meanwhile, a boat approaches, so the drawbridge is raised by means of a cable attached to the end opposite the hinge (see A loaded cement mixer drives onto an old figure below). The drawbridge is 40.0 m long and has a mass of 12,000 kg; its center of gravity is at its midpoint. The cement mixer, with driver, has mass 30,000 kg. When the drawbridge has been raised to an angle of 30° above the horizontal, the cable makes an angle of 70° with the surface of the bridge. T 70° k10.0m 40.0 m 30 (i) Sketch the free-body diagram (FBD) of the drawbridge with complete force labels. (ii) (ii) Determine the moment arm () of each force. Show complete solution. Put the results in a table. Determine the sign of the torque, based on the direction of rotation of the beam that is caused by each torque. Indicate these on your FBD. Indicate the signs of the torques in the table of results. What is the tension (T) in the cable when the drawbridge is held in this position? What are the horizontal and vertical components of the force the hinge (Fpx and Fpy) exerts on the drawbridge? (iv) (v)
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